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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="rltopsp1.html#NM1" title="RLTOPSP1:NM.1">LinearTopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a> <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds   <a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">X</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a></span><br/><b>let </b><font color="Maroon" title="c2">r</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a> <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c4">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x2</font> implies <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:95_1"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 <b>and </b><br/><a NAME="E2:95_1"/><i><font color="Green" title="E59">A2</font></i>: 
<font color="Maroon" title="c4">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 <b>and </b><br/><a NAME="E3:95_1"/><i><font color="Green" title="E60">A3</font></i>: 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font></span><br/><b>reconsider </b><font color="Maroon" title="c5">x1'</font> = <font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c6">x2'</font> = <font color="Maroon" title="c4">x2</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E1:95_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="#E2:95_1"><i><font color="Green" title="E59">A2</font></i></a></i>;<br/><a NAME="E5:95_1"/>
( <span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c5">x1'</font> &amp; <span class="p1">(<span class="default"><a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">x2'</font> )
 <b>by </b><i><a class="ref" href="rltopsp1.html#D13" target="_self" title="RLTOPSP1:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E6:95_1"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="#E3:95_1"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="rlvect_1.html#T50" title="RLVECT_1:th.50">RLVECT_1:50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:95"/>
 <a href="rltopsp1.html#K4" title="RLTOPSP1:func.4">mlt</a> <font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">X</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="ref" href="funct_2.html#T25" title="FUNCT_2:th.25">FUNCT_2:25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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